[stein-shakarchi] complex analysis

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1、COMPLEXANALYSISIbookrootOctober20,2007PrincetonLecturesinAnalysisIFourierAnalysis:AnIntroductionIIComplexAnalysisIIIRealAnalysis:MeasureTheory,Integration,andHilbertSpacesPrincetonLecturesinAnalysisIICOMPLEXANALYSISEliasM.Stein&RamiShakarchiPRINCETONUNIVERSI

2、TYPRESSPRINCETONANDOXFORDCopyright©2003byPrincetonUniversityPressPublishedbyPrincetonUniversityPress,41WilliamStreet,Princeton,NewJersey08540IntheUnitedKingdom:PrincetonUniversityPress,6OxfordStreet,Woodstock,OxfordshireOX201TWAllRightsReservedLibraryofCongr

3、essControlNumber2005274996ISBN978-0-691-11385-2BritishLibraryCataloging-in-PublicationDataisavailableThepublisherwouldliketoacknowledgetheauthorsofthisvolumeforprovidingthecamera-readycopyfromwhichthisbookwasprintedPrintedonacid-freepaper.∞press.princeton.ed

4、uPrintedintheUnitedStatesofAmerica5791086TomygrandchildrenCarolyn,Alison,JasonE.M.S.TomyparentsMohamed&MireilleandmybrotherKarimR.S.ForewordBeginninginthespringof2000,aseriesoffourone-semestercoursesweretaughtatPrincetonUniversitywhosepurposewastopresent,ina

5、nintegratedmanner,thecoreareasofanalysis.Theobjectivewastomakeplaintheorganicunitythatexistsbetweenthevariouspartsofthesubject,andtoillustratethewideapplicabilityofideasofanalysistootherfieldsofmathematicsandscience.Thepresentseriesofbooksisanelaborationofthe

6、lecturesthatweregiven.Whilethereareanumberofexcellenttextsdealingwithindividualpartsofwhatwecover,ourexpositionaimsatadifferentgoal:pre-sentingthevarioussub-areasofanalysisnotasseparatedisciplines,butratherashighlyinterconnected.Itisourviewthatseeingtheserela

7、tionsandtheirresultingsynergieswillmotivatethereadertoattainabetterunderstandingofthesubjectasawhole.Withthisoutcomeinmind,wehaveconcentratedonthemainideasandtheoremsthathaveshapedthefield(sometimessacrificingamoresystematicapproach),andwehavebeensensitivetoth

8、ehistoricalorderinwhichthelogicofthesubjectdeveloped.Wehaveorganizedourexpositionintofourvolumes,eachreflectingthematerialcoveredinasemester.Theircontentsmaybebroadlysum-marizedasfollows:I.Fourie